A semi-circular ring has mass m and radius R as shown in figure. Let `I_(1),I_(2) ,I_(3) " and "I_(4)` be the moments of inertia about the four axes as shown . Axis 1 passes through centre and is perpendicular to plane of ring. Then , match the following.

Explanation

(A- R,B -P,C -P,D -Q)
Place another identical semicircular ring to complete the circle of mass M=2m.
Both the halves have same amount of inertia by symmetry. For the complete circle, we know
`I_("axis") = MR^(2), I_(dis) = MR^(2)//2`

`rArr I_(1) + I_(1) = (2m)R^(2) rArr I_(1) = mR^(2)`
`I_(2) + I_(2) = (2m R^(2))/2 rArr I_(2) = (mR^(2))/2`
`I_(3) + I_(3) = (2m R^(2))/2 rArr I_(3) = (mR^(2))/2`
`I_(4) = I_(3) + mR^(2)` [By parallel axis theorem) `=3/2 mR^(2)`